#include "blaswrap.h"
#include "f2c.h"

/* Subroutine */ int zggqrf_(integer *n, integer *m, integer *p, 
	doublecomplex *a, integer *lda, doublecomplex *taua, doublecomplex *b,
	 integer *ldb, doublecomplex *taub, doublecomplex *work, integer *
	lwork, integer *info)
{
/*  -- LAPACK routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       June 30, 1999   


    Purpose   
    =======   

    ZGGQRF computes a generalized QR factorization of an N-by-M matrix A   
    and an N-by-P matrix B:   

                A = Q*R,        B = Q*T*Z,   

    where Q is an N-by-N unitary matrix, Z is a P-by-P unitary matrix,   
    and R and T assume one of the forms:   

    if N >= M,  R = ( R11 ) M  ,   or if N < M,  R = ( R11  R12 ) N,   
                    (  0  ) N-M                         N   M-N   
                       M   

    where R11 is upper triangular, and   

    if N <= P,  T = ( 0  T12 ) N,   or if N > P,  T = ( T11 ) N-P,   
                     P-N  N                           ( T21 ) P   
                                                         P   

    where T12 or T21 is upper triangular.   

    In particular, if B is square and nonsingular, the GQR factorization   
    of A and B implicitly gives the QR factorization of inv(B)*A:   

                 inv(B)*A = Z'*(inv(T)*R)   

    where inv(B) denotes the inverse of the matrix B, and Z' denotes the   
    conjugate transpose of matrix Z.   

    Arguments   
    =========   

    N       (input) INTEGER   
            The number of rows of the matrices A and B. N >= 0.   

    M       (input) INTEGER   
            The number of columns of the matrix A.  M >= 0.   

    P       (input) INTEGER   
            The number of columns of the matrix B.  P >= 0.   

    A       (input/output) COMPLEX*16 array, dimension (LDA,M)   
            On entry, the N-by-M matrix A.   
            On exit, the elements on and above the diagonal of the array   
            contain the min(N,M)-by-M upper trapezoidal matrix R (R is   
            upper triangular if N >= M); the elements below the diagonal,   
            with the array TAUA, represent the unitary matrix Q as a   
            product of min(N,M) elementary reflectors (see Further   
            Details).   

    LDA     (input) INTEGER   
            The leading dimension of the array A. LDA >= max(1,N).   

    TAUA    (output) COMPLEX*16 array, dimension (min(N,M))   
            The scalar factors of the elementary reflectors which   
            represent the unitary matrix Q (see Further Details).   

    B       (input/output) COMPLEX*16 array, dimension (LDB,P)   
            On entry, the N-by-P matrix B.   
            On exit, if N <= P, the upper triangle of the subarray   
            B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T;   
            if N > P, the elements on and above the (N-P)-th subdiagonal   
            contain the N-by-P upper trapezoidal matrix T; the remaining   
            elements, with the array TAUB, represent the unitary   
            matrix Z as a product of elementary reflectors (see Further   
            Details).   

    LDB     (input) INTEGER   
            The leading dimension of the array B. LDB >= max(1,N).   

    TAUB    (output) COMPLEX*16 array, dimension (min(N,P))   
            The scalar factors of the elementary reflectors which   
            represent the unitary matrix Z (see Further Details).   

    WORK    (workspace/output) COMPLEX*16 array, dimension (LWORK)   
            On exit, if INFO = 0, WORK(1) returns the optimal LWORK.   

    LWORK   (input) INTEGER   
            The dimension of the array WORK. LWORK >= max(1,N,M,P).   
            For optimum performance LWORK >= max(N,M,P)*max(NB1,NB2,NB3),   
            where NB1 is the optimal blocksize for the QR factorization   
            of an N-by-M matrix, NB2 is the optimal blocksize for the   
            RQ factorization of an N-by-P matrix, and NB3 is the optimal   
            blocksize for a call of ZUNMQR.   

            If LWORK = -1, then a workspace query is assumed; the routine   
            only calculates the optimal size of the WORK array, returns   
            this value as the first entry of the WORK array, and no error   
            message related to LWORK is issued by XERBLA.   

    INFO    (output) INTEGER   
             = 0:  successful exit   
             < 0:  if INFO = -i, the i-th argument had an illegal value.   

    Further Details   
    ===============   

    The matrix Q is represented as a product of elementary reflectors   

       Q = H(1) H(2) . . . H(k), where k = min(n,m).   

    Each H(i) has the form   

       H(i) = I - taua * v * v'   

    where taua is a complex scalar, and v is a complex vector with   
    v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),   
    and taua in TAUA(i).   
    To form Q explicitly, use LAPACK subroutine ZUNGQR.   
    To use Q to update another matrix, use LAPACK subroutine ZUNMQR.   

    The matrix Z is represented as a product of elementary reflectors   

       Z = H(1) H(2) . . . H(k), where k = min(n,p).   

    Each H(i) has the form   

       H(i) = I - taub * v * v'   

    where taub is a complex scalar, and v is a complex vector with   
    v(p-k+i+1:p) = 0 and v(p-k+i) = 1; v(1:p-k+i-1) is stored on exit in   
    B(n-k+i,1:p-k+i-1), and taub in TAUB(i).   
    To form Z explicitly, use LAPACK subroutine ZUNGRQ.   
    To use Z to update another matrix, use LAPACK subroutine ZUNMRQ.   

    =====================================================================   


       Test the input parameters   

       Parameter adjustments */
    /* Table of constant values */
    static integer c__1 = 1;
    static integer c_n1 = -1;
    
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
    /* Local variables */
    static integer lopt, nb;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    extern /* Subroutine */ int zgeqrf_(integer *, integer *, doublecomplex *,
	     integer *, doublecomplex *, doublecomplex *, integer *, integer *
	    ), zgerqf_(integer *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, doublecomplex *, integer *, integer *);
    static integer nb1, nb2, nb3, lwkopt;
    static logical lquery;
    extern /* Subroutine */ int zunmqr_(char *, char *, integer *, integer *, 
	    integer *, doublecomplex *, integer *, doublecomplex *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, integer *);


    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    --taua;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    --taub;
    --work;

    /* Function Body */
    *info = 0;
    nb1 = ilaenv_(&c__1, "ZGEQRF", " ", n, m, &c_n1, &c_n1, (ftnlen)6, (
	    ftnlen)1);
    nb2 = ilaenv_(&c__1, "ZGERQF", " ", n, p, &c_n1, &c_n1, (ftnlen)6, (
	    ftnlen)1);
    nb3 = ilaenv_(&c__1, "ZUNMQR", " ", n, m, p, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
    i__1 = max(nb1,nb2);
    nb = max(i__1,nb3);
/* Computing MAX */
    i__1 = max(*n,*m);
    lwkopt = max(i__1,*p) * nb;
    work[1].r = (doublereal) lwkopt, work[1].i = 0.;
    lquery = *lwork == -1;
    if (*n < 0) {
	*info = -1;
    } else if (*m < 0) {
	*info = -2;
    } else if (*p < 0) {
	*info = -3;
    } else if (*lda < max(1,*n)) {
	*info = -5;
    } else if (*ldb < max(1,*n)) {
	*info = -8;
    } else /* if(complicated condition) */ {
/* Computing MAX */
	i__1 = max(1,*n), i__1 = max(i__1,*m);
	if (*lwork < max(i__1,*p) && ! lquery) {
	    *info = -11;
	}
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("ZGGQRF", &i__1);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     QR factorization of N-by-M matrix A: A = Q*R */

    zgeqrf_(n, m, &a[a_offset], lda, &taua[1], &work[1], lwork, info);
    lopt = (integer) work[1].r;

/*     Update B := Q'*B. */

    i__1 = min(*n,*m);
    zunmqr_("Left", "Conjugate Transpose", n, p, &i__1, &a[a_offset], lda, &
	    taua[1], &b[b_offset], ldb, &work[1], lwork, info);
/* Computing MAX */
    i__1 = lopt, i__2 = (integer) work[1].r;
    lopt = max(i__1,i__2);

/*     RQ factorization of N-by-P matrix B: B = T*Z. */

    zgerqf_(n, p, &b[b_offset], ldb, &taub[1], &work[1], lwork, info);
/* Computing MAX */
    i__2 = lopt, i__3 = (integer) work[1].r;
    i__1 = max(i__2,i__3);
    work[1].r = (doublereal) i__1, work[1].i = 0.;

    return 0;

/*     End of ZGGQRF */

} /* zggqrf_ */

